Long ago, in https://graphics.stanford.edu/~boulos/papers/brdftog.pdf we tried to trade off energy conservation and data reproduction at the cost of reciprocity.

In the end, nobody actually cared about automatically fitting material data from BRDFs or if they do, they actually prefer a symmetric and conserving-enough BSDF, which is what most future research improved. In particular, breaking symmetry means making bidirectional path tracing and other techniques kinda weird.